{
  "id": "1102.4635",
  "version": "v1",
  "published": "2011-02-22T22:35:48.000Z",
  "updated": "2011-02-22T22:35:48.000Z",
  "title": "Outer Billiards on the Penrose Kite: Compactification and Renormalizaiton",
  "authors": [
    "Richard Evan Schwartz"
  ],
  "comment": "This is an extremely long paper -- 142 pages. It might be better as a monograph. I have tried to make the paper as modular as possible, isolating the computer-aided parts into clearly-defined units",
  "categories": [
    "math.DS"
  ],
  "abstract": "In this long paper we give a fairly complete analysis of outer billiards on the Penrose kite. Our analysis reveals that this 2-dimensional non-compact system has a 3-dimensional compactification, a certain polyhedron exchange map, and that this compactification has a renormalization scheme. These two features allow us to make some sharp statements concerning the distribution, large-scale geometry, fine-scale geometry, and hidden algebraic symmetries of the orbits. For instance, one of our results is that the union of the unbounded orbits has Hausdorff dimension 1. We give a computer-aided proof of the results concerning the compactification and the renormalization. This proof involves finitely many calculations done with exact integer arithmetic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-02-22T22:35:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "penrose kite",
      "outer billiards",
      "compactification",
      "renormalizaiton",
      "polyhedron exchange map"
    ],
    "tags": [
      "monograph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 142,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.4635S"
    }
  }
}